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Sample Size Calculaton

sample_size.Rd

Calculate the sample size required from a population to estimate the prevalence of a dichotomous variable to a given degree of absolute precision and with a specified level of confidence.

Usage

sample_size(Pexp = 0.5, d = 0.05, N = NULL, conf_level = 0.95)

Arguments

Pexp

numeric (or numeric vector with all values) between 0 and 1 representing the expected prevalence; default 0.5.

d

a positive numeric (or numeric vector with all values) greater than zero representing the desired absolute precision; default 0.05 .

N

either NULL for a large (theoretically infinite) population or a positive integer (or integer vector with all values) greater than zero representing the population size; default NULL.

conf_level

the confidence level(s) required; default 0.95.

Value

A numeric (or numeric vector) giving the required sample size(s).

Details

For large study populations, the sample size, n, may be calculated as: -

$$n = \displaystyle \frac{z^{2}P_{exp}(1-P_{exp})}{d^{2}}$$

where \(P_{exp}\) is the expected prevalence, z is the quantile of the normal distribution corresponding to the confidence level required and d is the desired absolute precision.

For relatively small study populations of size N, the value of n may be adjusted thus: -

$$n_{adj} = \displaystyle \frac{n.N}{n + N}$$

Note

Sample Size Calculator at www.calculator.net has further useful information on derivation.

References

Thrusfield, M., Christley, R. In Veterinary Epidemiology 4th Edn. John Wiley & Sons Ltd. 2018. (See Ch.13.) doi:10.1002/9781118280249 .

See also

Other sample-size: design_effect()

Examples

## Infinite population
sample_size()         ## desired absolute precision 0.05 (default)
#> [1] 385
sample_size(d = 0.1)  ## desired absolute precision 0.1
#> [1] 97

## Population = 500, 750 or 1000
sample_size(N = c(500L, 750L, 1000L))
#> [1] 218 255 278

## Expected prevalence = 0.125, 0.25, 0.50, 0.75 or 0.875
## Note symmetry of resulting sample sizes
sample_size(Pexp = c(0.125, 0.25, 0.50, 0.75, 0.875))
#> [1] 169 289 385 289 169

## Desired absolute precision = 1%, 5%, 10%, 20%
sample_size(d = c(0.01, 0.05, 0.1, 0.2))
#> [1] 9604  385   97   25